| 1. |
- Aggestam, Emil, 1992, et al.
(författare)
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Numerical model reduction with error control in computational homogenization of transient heat flow
- 2017
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - : Elsevier BV. - 0045-7825. ; 326, s. 193-222
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Tidskriftsartikel (refereegranskat)abstract
- Numerical Model Reduction (NMR) is exploited for solving the finite element problem on a Representative Volume Element (RVE) that arises from the computational homogenization of a model problem of transient heat flow. Since the problem is linear, an orthogonal basis is obtained via the classical method of spectral decomposition. A symmetrized version of the space–time variational format is adopted for estimating the error from the model reduction in (i) energy norm and in (ii) given Quantities of Interest. This technique, which was recently developed in the context of the (non-selfadjoint) stationary diffusion–convection problem, is novel in the present context of NMR. By considering the discrete, unreduced, model as exact, we are able to obtain guaranteed bounds on the error while using only the reduced basis and with minor computational effort. The performance of the error estimates is demonstrated via numerical results, where the subscale is modeled in both one and three spatial dimensions.
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| 2. |
- Ansin, Caroline, 1996, et al.
(författare)
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Fast simulation of 3D elastic response for wheel–rail contact loading using Proper Generalized Decomposition
- 2023
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - 0045-7825. ; 417
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Tidskriftsartikel (refereegranskat)abstract
- To increase computational efficiency, we adopt Proper Generalized Decomposition (PGD) to solve a reduced-order problem of the displacement field for a three-dimensional rail head exposed to different contact scenarios. The three-dimensional solid rail head is modeled as a two-dimensional cross-section, with the coordinate along the rail being treated as a parameter in the PGD approximation. A novel feature is that this allows us to solve the full three-dimensional model with a nearly two-dimensional computational effort. Additionally, we incorporate the distributed contact load predicted from dynamic vehicle-track simulations as extra coordinates in the PGD formulation, using a semi-Hertzian contact model. The problem is formulated in two ways; one general ansatz which considers the treatment of numerous parameters, some of which exhibit a linear influence, and a linear ansatz where multiple PGD solutions are solved for. In particular, situations where certain parameters become invariant are handled. We assess the accuracy and efficiency of the proposed strategy through a series of verification examples. It is shown that the PGD solution converges towards the FE solution with reduced computational cost. Furthermore, solving for the PGD approximation based on load parameterization in an offline stage allows expedient handling of the wheel-rail contact problem online.
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| 3. |
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| 4. |
- DAWODY, JAZAER, 1959, et al.
(författare)
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An integrated system for energy-efficient exhaust aftertreatment for heavy-duty vehicles
- 2015
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Ingår i: Renewable Energy in the Service of Mankind. - Cham : Springer International Publishing. - 9783319177779 - 9783319177762 ; , s. 133-143
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- © Springer International Publishing Switzerland 2015. This chapter presents a unique system approach applied in a joint academic- industrial research programme, E4 Mistra, to attain the goals of high energy efficiency and low emissions in an exhaust aftertreatment system for heavy-duty vehicles. The high energy efficiency is achieved by heat recuperation, onboard hydrogen production for NOx reduction, and by finding new solutions for making the aftertreatment system active at low exhaust temperatures. To reach low particulate emissions, a mechanical filter using a sintered metal powder is developed and coated with catalytic material to improve the soot oxidation efficiency. Low NOx emissions are achieved by an efficient NOx reduction catalyst. The integrated E4 Mistra system comprises four technological advances: thermoelectric (TE) materials for heat recuperation, catalytic reduction of NOx over innovative catalyst substrates using either the onboard diesel or biodiesel, H2 from a high-efficiency fuel reformer, and particulate filtration over a porous metal filter. The TE materials are used in a TE generator (TEG) which converts thermal energy into electricity. The TEG is used to recuperate heat from the exhaust-gas recirculation (EGR) circuit of heavy-duty trucks and is expected to generate ~1 kW electric power from 20 kW heat in the exhaust gas. The TEG is integrated in a plate heat exchanger (HEX) designed particularly for this application. Apart from the knowledge and experiences in TEG and heat exchange technologies, a thorough fluid dynamics and TE analysis are performed in this project to understand the governing processes and optimize the system accordingly. The components of the E4 Mistra system are explained in the chapter in addition to test results, which show the system's capacity for H2 production, NOx conversion, particulate matter filtration and soot oxidation, and finally electric power generation via heat recuperation from the exhaust gas using the developed TEG-HEX system.
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| 5. |
- Ekre, Fredrik, 1992, et al.
(författare)
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A posteriori error estimation for numerical model reduction in computational homogenization of porous media
- 2020
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 0029-5981 .- 1097-0207. ; 121:23, s. 5350-5380
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Tidskriftsartikel (refereegranskat)abstract
- Numerical model reduction is adopted for solving the microscale problem that arizes from computational homogenization of a model problem of porous media with displacement and pressure as unknown fields. A reduced basis is obtained for the pressure field using (i) spectral decomposition (SD) and (ii) proper orthogonal decomposition (POD). This strategy has been used in previous work—the main contribution of this article is the extension with an a posteriori estimator for assessing the error in (i) energy norm and in (ii) a given quantity of interest. The error estimator builds on previous work by the authors; the novelty presented in this article is the generalization of the estimator to a coupled problem, and, more importantly, to accommodate the estimator for a POD basis rather than the SD basis. Guaranteed, fully computable and low-cost bounds are derived and the performance of the error estimates is demonstrated via numerical results.
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| 6. |
- Ekre, Fredrik, 1992, et al.
(författare)
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Combining spectral and POD modes to improve error estimation of numerical model reduction for porous media
- 2022
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Ingår i: Computational Mechanics. - : Springer Science and Business Media LLC. - 1432-0924 .- 0178-7675. ; 69:3, s. 767-786
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Tidskriftsartikel (refereegranskat)abstract
- Numerical model reduction (NMR) is used to solve the microscale problem that arises from computational homogenization of a model problem of porous media with displacement and pressure as unknown fields. The reduction technique and an associated error estimator for the NMR error have been presented in prior work, where both spectral decomposition (SD) and proper orthogonal decomposition (POD) were used to construct the reduced basis. It was shown that the POD basis performs better w.r.t. minimizing the residual, but the SD basis has some advantageous properties for the estimator. Since it is the estimated error that will govern the error control, the most efficient procedure is the one that results in the lowest error bound. The main contribution of this paper is further development of the previous work with a proposed combined basis constructed using both SD and POD modes together with an adaptive mode selection strategy. The performance of the combined basis is compared to (i) the pure SD basis and (ii) the pure POD basis via numerical examples. The examples show that it is possible to find a combination of SD/POD modes which is improved, i.e. it yields a smaller estimate, compared to the cases of pure SD or pure POD.
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| 7. |
- Ekre, Fredrik, 1992, et al.
(författare)
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Efficient Two-Scale Modeling of Porous Media Using NumericalModel Reduction with Fully Computable Error Bounds
- 2022
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Ingår i: Current Trends and Open Problems in Computational Mechanics. - Cham : Springer International Publishing. ; , s. 121-129
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- The microscale problem arizing from computational homogenization of porous media problems is solved by adopting the concept of Numerical Model Reduction. Thereby, the displacement and pore pressure are the unknown fields. A suitable reduced basis is constructed for the pore pressure approximation using Proper Orthogonal Decomposition (POD), whereby it is possible to compute the appropriate basis for the displacement field in the spirit of Nonlinear Transformation Field Analysis (NTFA). Inexpensive fully computable error bounds are obtainable, and the performance of the error estimates is illustrated in this paper.
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| 8. |
- Ekre, Fredrik, 1992, et al.
(författare)
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Numerical Model Reduction with error estimation for computational homogenization of non-linear consolidation
- 2022
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - : Elsevier BV. - 0045-7825. ; 389
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Tidskriftsartikel (refereegranskat)abstract
- Numerical Model Reduction (NMR) is adopted for solving the non-linear microscale problem that arises from computational homogenization of a model problem of porous media with displacement and pressure as unknown fields. A reduced basis is obtained for the pressure field using Proper Orthogonal Decomposition and the pertinent displacement basis is obtained using Nonuniform Transformation Field Analysis. An explicit, fully computable, a posteriori error estimator is derived based on the linearized error equation for quantification of the NMR error in terms of a suitably chosen energy norm. The performance of the error estimates is demonstrated via a set of numerical examples with varying load amplitudes.
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| 9. |
- Ekre, Fredrik, 1992, et al.
(författare)
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On error controlled numerical model reduction in FE2-analysis of transient heat flow
- 2019
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 0029-5981 .- 1097-0207. ; 119:1, s. 38-73
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Tidskriftsartikel (refereegranskat)abstract
- Numerical model reduction is exploited for solving the two-scale problem that arises from the computational homogenization of a model problem of transient heat flow. Since the problem is linear, an orthogonal basis is obtained via the method of spectral decomposition. A key feature is the construction of a symmetrized version of the space-time variational format, by which it is possible to estimate the error from the model reduction in (i) energy norm and in (ii) a given quantity of interest. In previous work by the authors, this strategy has been applied to the solution of an individual representative volume element problem, whereas the error transport to the macroscale problem in the finite element squared (FE2) approach was ignored. In this paper, such transport of error is included in the error estimate. It is remarkable that it is (still) possible to obtain guaranteed bounds on the error, as compared to the fully resolved discrete finite element problem, while using only the reduced basis and with minor extra computational effort. The performance of the error estimates is demonstrated via numerical results, whereby the subscale is modeled in three dimensions, whereas the macroscale problem is either one or two dimensional.
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| 10. |
- Heintz, Per, 1975, et al.
(författare)
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Adaptive strategies and error control for computing material forces in fracture mechanics
- 2004
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 0029-5981 .- 1097-0207. ; 60:7, s. 1287-1299
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Tidskriftsartikel (refereegranskat)abstract
- The concept of material forces pertains to a variation of the inverse motion map while the placement field is kept fixed. From the weak formulation of the self-equilibrating Eshelby (material) stress tensor it turns out that the classical J-integral formulations in fracture mechanics are just special cases due to the choice of particular weight functions. In this contribution, we discuss a posteriori error control of the material forces as part of an adaptive strategy to reduce the discretization error to an acceptable level. The data of the dual problem involves the quite non-conventional tangent stiffness of the (material) Eshelby stress tensor with respect to a variation of the (physical) strain field. The suggested strategy is applied to the common fracture mechanics problem of a single-edged crack, whereby different strategies for computing the J-integral are compared. We also consider the case in which the crack edges are not parallel, i.e. a notch.
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